A Simple Mathematical Model for Flood Control by a Dry Dam

Abstract

At the same time that the estimated risk of natural disasters is increasing due to global warming, the capacity to prevent disasters in Japan has been weakened due to infrastructure degradation and population aging. To reduce the damage caused by flooding, flood control dams without a slide gate in a spillway, known as “dry dams,” have been planned and built on some sites in Japan. In this study, a simple mathematical model for flood control by a dry dam is proposed, aiming to encourage the construction of such dams. An implicit integral equation that is based on the continuity equation and simulates flood control by a dry dam is analytically derived. This equation can be easily solved by a spreadsheet program, making the mathematical models widely accessible, particularly to hydraulic engineers and students. The model’s results are compared with laboratory experimental results and the output of a numerical simulation. The results show that the accuracy of the model is quite good, especially in its prediction of the maximum water level of dam reservoirs, meaning that the peak discharge during a flood can be predicted to high accuracy by using this simple mathematical model.